Simulating Earthquakes by Combining Analytical Models with Physical Structures

By Thomas M. Marullo, Lehigh University

Civil engineers use complex analytical and numerical models to predict how bridges, buildings, and other structures will behave during earthquakes and to design earthquake-resistant structures. The large scale of the structures and the magnitude of forces needed to simulate a seismic event make testing and validating these models a significant challenge.

To meet this challenge and increase the accuracy of earthquake simulations, Lehigh University established the Real-Time Multi-Directional (RTMD) earthquake simulation facility at the Advanced Technology for Large Structural Systems (ATLSS) Engineering Research Center. The facility is part of the George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES) Program. Housed in a repurposed steel plant, it includes a reaction wall and hydraulic actuators capable of applying force to a structure from three directions. With a floor area of approximately 100 feet by 40 feet, and reaction walls up to 50 feet high, the facility is among the largest of its kind (Figure 1). It has been used to test parts of ships’ hulls, bridge decks, shear walls, and four-story buildings (Figure 2).

Figure 1. The L-shaped ATLSS reaction wall.
Figure 1. The L-shaped ATLSS reaction wall.
Figure 2. A steel frame with actuators set up for testing at ATLSS.
Figure 2. A steel frame with actuators set up for testing at ATLSS.

Lehigh graduate students and researchers use Simulink® to develop models of large-scale structures and the actuator controllers that replicate seismic activity. Data gathered from the sensors is postprocessed in MATLAB®. xPC Target enables the team to conduct real-time hybrid tests that combine physical structures with analytical models.

Hardware-in-the-Loop Simulation of Buildings and Bridges

Software engineers frequently use hardware-in-the-loop simulations to verify their designs. They might test an embedded system, for example, by connecting it to a simulation of the remaining design running in real time. NEES experiments use an analogous approach. In our case, we connect a physical specimen–part of a building or bridge–to a simulation of the rest of the building or bridge.

In many of our experiments, the specimen is a damper, which helps stabilize a building during an earthquake by absorbing and dissipating seismic energy. Simple dampers are rubber-filled steel tubes connected to a building’s floor. More advanced dampers use magnetorheological (MR) fluid, which increases in viscosity when exposed to a magnetic field.

In a typical experiment, the researchers first characterize the damper and its response to applied loads. Actuators excite the damper, and sensors measure temperature, load, strain, or displacement. The characterization data is analyzed using MATLAB and System Identification Toolbox, and the results of this analysis are used to construct a simple model of the damper.

Next, the team constructs a model of the complete structure in Simulink. This model uses a hybrid finite element method technique in which the frame of a structure is represented by nodes and the elements connecting those nodes. We run simulations in Simulink to test the basic operation of the model.

To run the real-time hybrid simulation, we replace the simple damper model with the actual damper in the ATLSS facility (Figure 3), leaving what we call the analytical substructure model. Using a historical earthquake record, our Simulink control model generates displacement commands and sends them to the analytical substructure model and to the hydraulic control system that excites the specimen. The results from the analytical structure model and the specimen’s reaction to the displacement commands are fed back to the Simulink control model, where they are integrated with the earthquake data to calculate the next set of displacement commands.

Figure 3. A block diagram of the real-time hybrid simulation flow.
Figure 3. A block diagram of the real-time hybrid simulation flow.

Real-Time Simulation with xPC Target

The ability to conduct simulations in real time improves the accuracy, validity, and reliability of our results. We use xPC Target to execute our Simulink models in real time on turnkey target computers. In our setup (Figure 4), the Simulink control model runs on one or more xPC Target computers and communicates with the ATLSS hydraulic actuators via a Shared Common Random Access Memory Network (SCRAMNet). We use web cameras to make time-lapse videos of our experiments and to enable researchers not present in the lab to view experiments. Data is gathered from the sensors and instruments using Data Acquisition Toolbox.

Figure 4. The ATLSS infrastructure.
Figure 4. The ATLSS infrastructure. The data streamer streams data over the Internet to users in real time. The PID controller is used to control the hydraulic actuators.

In some cases, we need to bypass SCRAMNet and send signals directly to the specimen under test. For example, when the specimen is an MR fluid damper, our control system adjusts the damper’s stiffness by using Data Acquisition Toolbox to control the electrical current applied to the damper.

Our experiments are not limited to dampers. Recently, we tested the performance of some commercially manufactured pipe materials and couplings. We conducted real-time tests of a piping system in a three-story building during a simulated earthquake (Figure 5). The tests validated the manufacturer’s in-house testing, and gave them added confidence that their products would perform safely during earthquakes.

Figure 5. Pipes and couplings under test at ATLSS.
Figure 5. Pipes and couplings under test at ATLSS.

Analyzing Simulation Results

Students and researchers use MATLAB to postprocess the large volumes of data collected from ATLSS sensors during each experiment. MATLAB plots enable them to visualize results and gain insights into the specimen’s response to seismic forces (Figure 6). The team estimates power spectral densities and applies filters to the results using Signal Processing Toolbox. Further statistical analysis is performed using Statistics Toolbox.

Figure 6. Plot of actuator displacement in millimeters as a function of time.
Figure 6. Plot of actuator displacement in millimeters as a function of time, one of the many plots we use to visualize experimental data.

The results are used to improve the stability of structures in subsequent experiments—and ultimately in the real-world—by repositioning dampers and by identifying the best type of damper to use in a particular structure. More broadly, the results yield validated Simulink models of those structures that engineers can use to determine how their designs will respond during an earthquake.

Conducting Distributed Tests with Other Facilities

Some of the structures that we want to test exceed the capacity of our ATLSS facility. The span of a freeway bridge, for example, does not easily fit within our reaction wall. For the Multi-Site Soil-Structure-Foundation Interaction Test (MISST), we collaborated with the University of Illinois at Urbana–Champaign (UIUC) and Rensselaer Polytechnic Institute (RPI) to analyze part of the I-10 Santa Monica freeway that was damaged during the Northridge earthquake in 1994.

For this project, large-scale bridge pier specimens were constructed at UIUC and ATLSS, and RPI developed advanced models of the soil beneath the piers. The forces applied to the bridge piers were generated from seismic data of the actual earthquake and coordinated via the Internet. Lehigh and UIUC used MATLAB, Data Acquisition Toolbox, and Instrument Control Toolbox to control and coordinate the tests. To enable communication and synchronization among the sites, the tests were not conducted in real time; instead a 30-second test took about 3 hours to simulate. The piers failed just as the actual I-10 piers had, validating the simulation and making it possible to design and test solutions that will prevent such failures in future earthquakes.

Published 2012 - 92068v00

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